color image retrieval using hybrid graph representationimage.inha.ac.kr/paper/ivc99pik.pdf · 2017....

Color image retrieval using hybrid graph representation

In Kyu Parka,*, Il Dong Yunb, Sang Uk Leea

aSchool of Electrical Engineering, Seoul National University, Seoul 151-742, South KoreabDepartment of Control and Instrumentation Engineering, Hankuk University of F.S. Yongin, Yongin 449-791, South Korea

Received 2 April 1997; received in revised form 12 December 1997; accepted 10 June 1998

Abstract

In this paper, a robust color image retrieval algorithm is proposed based on the hybrid graph representation, i.e., a dual graph whichconsists of the Modified Color Adjacency Graph (MCAG) and Spatial Variance Graph (SVG). The MCAG, which is similar to the ColorAdjacency Graph (CAG) [6], is proposed to enhance the indexing ability and the database capacity, by increasing the feature dimension. Inaddition, the SVG is introduced, in order to utilize the geometric statistics of the chromatic segment in the spatial domain. In the matchingprocess, we expand the histogram intersection [2] into the graph intersection, in which graph matching is performed using simple matrixoperations. Intensive discussions and experimental results are provided to evaluate the performance of the proposed algorithm. Experimentsare carried out on the Swain’s test images and the Virage images, demonstrating that the proposed algorithm yields high retrievalperformance with tolerable computational complexity. It is also shown that the proposed algorithm works well, even if the query imageis corrupted. e.g., a large part of pixels is missing.q 1999 Elsevier Science B.V. All rights reserved.

Keywords:Color image retrieval algorithm; Hybrid graph representation; Modified color adjacency graph (MCAG); Spatial variance graph (SVG); Indexingability; Database capacity; Retrieval performance

1. Introduction

Image retrieval from a large database is an importantproblem as the application of multimedia technologyincreases [1]. In the traditional database system, a context-based query and retrieval scheme, based on the textual key-word or file name, is usually adopted. However, a visualdatabase is usually very large, so that such an approachrequires complicated preclassification and, furthermore,the same image might be described in different ways bydifferent people. In this context, a content-based imageretrieval technique is very attractive. Among several con-tents of image, the color histogram is known to provideuseful clues for measuring the similarity of two images,since it is robust to object distortion, including deformation,translation, rotation, occlusion, and scaling of the object.Moreover, image retrieval based on a histogram is veryfast, making a real-time implementation possible [2]. There-fore, many studies have reported on histogram-based colorimage retrieval techniques [2–4,8,9].

Swain and Ballard [2] proposed a color histogram basedon the so-calledcolor indexingalgorithm to identify color

images. The 3D histograms are generated for the input andmodel images in the database. Then attempts are made tomatch two images, employing the histogram intersectionmethod. The technique in Ref. [2] is very simple to imple-ment, while providing good performance. Punt andFinlayson [3] proposed thecolor constant color indexingalgorithm to take into account the effect of differentillumination. It is shown [3] that the differentiation of thelogarithm of the image is independent of the illuminationconditions, making illumination-invariant indexingpossible.

In addition to the color histogram itself, color adjacencyinformation is also used for indexing [5,6,8,16]. Ennesserand Medioni [5] developed a local histogram method tolocate an object in the color image, in which the co-occur-rence histogram is employed to increase the dimension ofthe feature space. Matas et al. [6] proposed the Color Adja-cency Graph (CAG), in which salient chromatic informationis carried by each node, while the reflectance ratio of theadjacent color components is employed for the attributes ofthe each edge. Note that Ref. [6] utilizes graph-matching, sothat an object could be labeled in the whole image. It isinteresting to note that several attempts have been maderecently to implement the image search engine on theworld wide web (WWW) [12–14].

0262-8856/99/$ - see front matterq 1999 Elsevier Science B.V. All rights reserved.PII: S0262-8856(98)00139-5

* Corresponding author.E-mail address:[email protected] (I.K. Park)

Image and Vision Computing 17 (1999) 465–474

IMAVIS 1590

The major issues which should be considered in imageretrieval are successful retrieval rate, matching speed, andthe capacity of the database. The retrieval rate is signifi-cantly affected by the deformation, rotation and translationof the object, noise addition, illumination changes, andvariation of viewpoint. Matching speed is determined bythe histogram quantization, database size, image size, andresolution. On the other hand, since the visual database isusually very large, the capacity of the indexing algorithm isof special interest [10]. This provokes the demand forincreasing the dimension of the feature space. This is themain motivation of the proposed algorithm in this paper.

In our approach, the relationship between two distinctnodes is properly modeled in both chromatic and spatialdomains. In the Modified Color Adjacency Graph (MCAG),the pixel adjacency of two chromatic regions is also taken intoaccount, in addition to the histogram itself. Before construct-ing the MCAG, an image needs to be processed in order toremove the noisy channel which lies on the boundary betweentwo adjacent chromatic regions. In our approach, the majorityfiltering technique [15] is employed to remove the noisechannel. It is found that the chromatic edges between theregions are enhanced significantly after applying the majorityfilter. In addition to the MCAG, the Spatial Variance Graph(SVG) is also proposed to improve the performance, in whichself and relational variance of chromatic regions are utilized.The proposed SVG differs from other previous work [7] inthat moment features are constructed using the distribution ofcolor pixels in the spatial domain. In the matching process,the cost is defined by the weighted sum of the graph inter-section results. Actually, the graph intersection is the general-ization of the histogram intersection [2]. Finally, each graphis relevantly interpreted in terms of the matrix form, and thenthe graph intersection is done by introducing a few matrixoperations.

This paper is organized as follows. In Section 2, theproposed algorithms, including the MCAG and the SVGrepresentations of an image, and matching technique arepresented in detail. Section 3 presents the experimentalresults of the proposed algorithm and comparison withother algorithms [2]. Thereafter, we give concludingremarks in Section 4.

2. The proposed algorithms

Content-based retrieval is a new paradigm in databasemanagement systems. When it comes to the ‘content’ ofan image, we mean the generic image properties, such ascolor, texture, shape and composition. Among these proper-ties, color provides direct and quick access to image, sincethe color is easy to process with a tolerable computationalcomplexity. In this context, the proposed graph representa-tion is based on the color distribution, i.e., a color histogramof the image. It is worth noting that the graph-basedapproach could be easily extended to other features.

Subsequently, we shall describe the proposed algorithmin detail. The flow chart for the proposed algorithm is shownin Fig. 1.

2.1. Preprocessing with majority filter

It is found that there exists a noisy channel near theboundary of adjacent chromatic regions. This stems fromthe blending effect of light and the CCD input characteris-tics. Thus, in order to acquire more reliable and noiselessgraph representation, the color image needs to be processedto yield a clear boundary between the regions. In ourapproach, the majority filtering technique [15] is employed,since all minor noise pixels can be merged with the majorpixels in the filtering window.

Let W be the filtering window, in which there existskdifferent chromatic components,C1,C2,…,Ck. Then themajority operator is defined as

M(P(x)) ¼Ci , Ni . Nj , 1 # j # k, j Þ i

P(x), otherwise,

((1)

whereNi is the pixel count ofCi in W.An example of the majority filtering is shown in Fig. 2, in

which upper-right part of Fig. 2a is illustrated in Fig. 2b. As

Fig. 1. The flowchart for the proposed algorithm.

Fig. 2. Majority filtering. (a) Real image; (b) upper-right region of (a)magnified; (c) filtering result of (b).

466 In Kyu Park et al. / Image and Vision Computing 17 (1999) 465–474

shown, a thin noisy channel lies between the blue andorange regions. However, after applying the majorityoperator, the noisy channel is significantly removed, asdepicted in Fig. 2c. This improves the chromatic adjacencybetween the regions, making the resultant graph representthe image more clearly.

2.2. Modified color adjacency graph (MCAG)

To represent a color image in the feature space, weintroduce the Modified Color Adjacency Graph (MCAG)representation. Since each quantized histogram bin ismapped into a node of the MCAG, there exist as manynodes as the number of effective histogram bins. In theMCAG, the node attribute encodes the pixel count of theRGB chromatic component, while the edge attribute denotesthe spatial adjacency of two color features. In theimplementation, we consider the color adjacency based oneight-connectivity. A 33 3 window is applied to everypixel in each region, in which the pixel count of the

neighboring region is added to the corresponding edgelabel. A simple image and its resultant MCAG are shownin Fig. 3.

Usually there are many nodes in the real image, so thatthe size of a graph also becomes very large. For instance, ifwe quantize each R, G, B axis into eight levels, the numberof histogram bins would be 512. Thus, there are 512 nodesand 130 816

¼512

2

! !

edges in the graph, requiring tremendous computationalburden to match all of the nodes and edges. Fortunately,however, the majority of the nodes and edges which canbe excluded before matching are found to be null. In ourapproach, a node is classified into an effective one when thecount of pixels in the node exceeds the given threshold. Thethreshold t is determined to be the maximum value,satisfying the need that the sum of node attributes above

Fig. 3. Simple example of the MCAG generation. (a) 103 10 image; (b) resultant MCAG.

Table 1The matrix representation of the MCAG in Figure 4

Index 0 147 148 149 163 166 171 193 194 228 235 243 300 301 365 373 437 438 446 506 507 510 511

0 82 64 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0147 98 10 0 0 0 0 0 0 94 0 0 48 9 16 0 8 9 9 0 0 0 0148 128 56 0 0 0 0 0 10 0 0 0 11 0 0 0 0 0 0 0 0 0149 180 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0163 80 0 26 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 0166 74 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0171 104 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 0193 48 22 0 0 0 0 0 0 0 0 0 0 0 0 0 0194 82 0 0 0 0 0 0 0 0 0 0 0 0 0 0228 264 0 0 117 34 27 8 8 18 0 0 0 0 0235 388 41 0 0 0 0 0 0 0 0 0 0 0243 118 0 0 0 0 0 0 0 0 0 0 0300 216 77 129 14 14 13 0 0 0 0 0301 80 112 0 0 16 0 0 0 0 0365 782 155 61 46 13 0 0 8 13373 186 57 62 8 0 0 0 0437 174 114 21 0 0 29 0438 396 89 0 0 64 68446 102 0 0 88 37506 716 143 0 0507 322 0 0510 628 205511 3388

467In Kyu Park et al. / Image and Vision Computing 17 (1999) 465–474

the threshold is greater than given fractionf of total pixels.More specifically,

t ¼ maxl

∑Ni.l

Ni

!. Nt·f

" #(2)

whereNi andNt denote theith node attribute and the totalpixel count, respectively.

Several advantages of the MCAG representation areexplained as follows. First, since the MCAG is based on acolor histogram, the advantages of the histogram indexingtechnique are also applicable. Next, the geometricalinformation can be taken into account, since the adjacencyof spatial regions is considered in the graph. In addition,since the graph representation can describe an image in acompact way, an effective matching procedure can beestablished.

Table 1 shows the matrix representation of the MCAG fora real image shown in Fig. 4. As is shown, the matrix size isquite small; there are only 23 nodes. In this case, the amountof image data is reduced to one-sixtieth of the original.Notice that the compression of the data is one of the crucialfactors when image retrieval is considered on the network.

2.3. Spatial variance graph (SVG)

Although the MCAG provides a representative model inboth histogram space and spatial domain, it is not sufficientto obtain the geometric statistics of each chromatic compo-nent. Since the spatial distribution of single color can beconsidered as another meaningful attribute of the node, adual graph representation is developed in our approach inaddition to the MCAG.

Fig. 5 illustrates the usefulness of the SVG, in which thehistogram intersection method [2] regards all the images asthe same one, since the pixel count of each region is fixedfrom image to image. On the other hand, the MCAGcannot distinguish (a) from (b), even though it can distin-guish (a) and (b) from (c) using color adjacency. However,we shall show that the employment of the statisticalcharacteristics of the chromatic regions in the spatialdomain makes it possible to obtain a unique graph foreach image.

First, let us consider two nodesk andl in the MCAG withtheir attributesNk andNl, respectively, forming two classesof pixels:Ck andCl. In the spatial domain, let us denote theimage coordinates of the pixel inCk andCl by Pi

k andPil ,

respectively. Then, the probability of class occurrence is

given by

qk ¼ Pr(Ck) ¼Nk

Nk þ Nl, (3)

ql ¼ Pr(Cl) ¼Nl

Nk þ Nl: (4)

In the image coordinates, first- and second-order statistics oftwo classes are given by

~mk ¼1Nk

∑Nk

i ¼ 1Pk

i (5)

~ml ¼1Nl

∑Nl

i ¼ 1Pl

i (6)

~mT ¼ qk~mk þ ql ~ml (7)

j2k ¼

1Nk

∑Nk

i ¼ 1(Pk

i )T(Pk

i ) ¹ ~mTk ~mk (8)

j2l ¼

1Nl

∑Nl

i ¼ 1(Pl

i)T(Pl

i) ¹ ~mTl ~ml : (9)

In order to evaluate the relational variance of two classes,we introduce the following discriminant criterion in thethresholding technique [11]:

j2W ¼ qkj

2k þ qlj

2l (10)

j2B ¼ qk(~mk ¹ ~mT)T(~mk ¹ ~mT) þ ql(~ml ¹ ~mT)T(~ml ¹ ~mT)

¼ qkql(~ml ¹ ~mk)T(~ml ¹ ~mk) ð11Þ

j2T ¼

1Nk þ Nl

∑Nk

i ¼ 1(Pk

i ¹ ~mT)T(Pki ¹ ~mT)

(

þ∑Nl

i ¼ 1(Pl

i ¹ ~mT)T(Pli ¹ ~mT)

)ð12Þ

wherejW2 , jB

2 , andjT2 denote the within-class variance, the

between-class variance, and the total variance of twoclasses, respectively. In fact, the following relationshipholds:

j2W þ j2

B ¼ j2T (13)

In the SVG, each node takes the self variance as its attribute,Fig. 4. An example of a real image.

Fig. 5. An example showing that the SVG is useful. (a,b) Images which canbe distinguished using the MCAG or the SVG. (c) Image which can bedistinguished employing the SVG.


and one of the relational variances serves as the edgeattribute. This provides a statistical model for the color dis-tribution in the spatial domain. It is experimentally foundthat the best matching performance is achieved by using thewithin-class variance, although the difference is not signifi-cantly distinguished. The SVG is invariant in translation androtation, if the geometric relationship of each regionremains unchanged, since the variance does not depend onpixel coordinates. However, when the input is scaled withrespect to the model image, the information contained in theSVG could be incorrect, due to the scaling. To compensatethe discrepancy, the SVG of the input should be normalized,simply by multiplying the ratio of the model image size tothe input image size.

2.4. Similarity metric

Since every model image in the database can be repre-sented by the MCAG and the SVG in off-line processing,the generation of the graph for database images does notaffect the matching complexity. In the implementation, theMCAG and the SVG are represented in the matrix form. Theadjacency matrixM MCAG and M SVG are considered, inwhich the diagonal and off-diagonal elements denote thenode and edge attributes, respectively. In addition, a selec-tion matrixS is considered to choose the effective nodes.Sis a diagonal binary matrix, in whichSi,i is 1, if the ith nodeis the effective one. Then, by multiplyingS to M MCAG andM SVG, we obtain the resultant matrix̄MMCAG andM̄SVG, asin Eq. (14), in which nonzero elements denote self orrelational attributes of the effective nodes and edges.

M̄ MCAG ¼ SMMCAGS

M̄SVG ¼ SMSVGS(14)

The similarity metric forM̄ (eitherM̄MCAG or M̄SVG) is, infact, the generalization of Swain’s; the histogram inter-section is expanded into the graph intersection. In otherwords, the similarity between the two graphs is measuredby the intersection of the graphs. Fig. 6 shows the procedurefor the similarity computation. Two graphs to be comparedare shown in Fig. 6a, in which dashed circles and linesdenote the null nodes and edges, respectively. The matrixrepresentation,̄M , of each graph is shown in Fig. 6b. Note thatthe common nodes and edges are distinguished by rectangles.

Before introducing the similarity metric, let us first definea few terms and operations for̄M as follows:

(1) NormkM k: the sum of all elements in upper triangularpart ofM .

(2) IntersectionM̄ 1 ∩ M̄ 2: reduced matrix with commonnodes and edges of both̄M 1 and M 2, in which the (i,j)element is the smaller one of two corresponding labels.For example, the intersection of matrices in Fig. 6b is

8 3

3 5

!:

(3) Norm of unionkM̄1 ∪ M̄ 2k :

kM̄ 1 ∪ M̄ 2k¼ kM̄ 1kþ kM̄ 2k¹ kM̄ 1 ∩ M̄ 2k (15)

Based on the above operations, the similarity metric is nowdefined, given by

S¼akM̄ INPUT

MCAG ∩ M̄MODELMCAG k

kM̄ INPUTMCAG ∪ M̄MODEL

MCAG kþ b

kM̄ INPUTSVG ∩ M̄MODEL

SVG kkM̄ INPUT

SVG ∪ M̄MODELSVG k

(16)

where the weightsa andb are usually chosen to be 1. Eachmetric in Eq. (16) increases from 0 to 1, as the imagesbecome more similar. For example, the computed similarity

Fig. 6. Computation of similarity. (a) Graph representations; (b) matrix representations of the graph in (a); (c) similarity computation.


of the graphs in Fig. 6 is 0.195, as shown in Fig. 6c. Noticethat, in Eq. (16), the similarityS is defined as the weightedsum of the metrics of the MCAG and SVG.

2.5. The complexity of the proposed algorithm

Now, let us briefly consider the complexity of the pro-posed graph matching. There are two computational com-plexity terms: graph generation timetg and graph matchingtime tm. Assuming there areM model images in the data-base, the approximated computational complexities for eachterm are approximatelytg ¼ O(NI

2) and tm ¼ O(M·NG2 ),

whereNI andNG denote the image and graph size, respec-tively. Thus, total complexity istg þ tm, which is slightlymore complex than Swain’s algorithm.

3. Experimental results

In this section, we explore several experiments todemonstrate the performance of the proposed algorithm.

Two databases are tested: Swain’s and Virage imagedatabase [12], which are shown in Figs. 7–10. Of the twodatabases, the Virage images are believed to be morenatural, since there is no black background in the Virageimage.

In the implementation, we employ the RGB coordinates.Although the HSI color coordinate is preferred in severalcases [8,13], we found that the indexing performance isalmost comparable. In our experiments, each chromaticaxis is quantized into eight levels, yielding 512 histogrambins. Thus, the maximum number of nodes in the graphcould be 512. However, as discussed previously, majorityof the nodes are found to be null. For instance, in the case ofSwain’s database, the average number of effective nodes isobserved only to be 108, even if we setf ¼ 1.0 in Eq. (2),i.e., all the non-empty nodes are regarded as effective. Theremaining others are all empty nodes, which are ignoredwhen storing and matching the graph.

The indexing capability is measured, in terms of the rank,the successful matching rate (SMR), and the average matchpercentile (AMP). The SMR is defined as the rate of perfect

Fig. 7. Swain’s image database [2].

Fig. 8. Swain’s input images [2].


Fig. 9. Virage image database [12].

Fig. 10. Example of the Virage input images (total 50 images) [12].

Table 3Indexing result with the Virage images (50 inputs, 104 models,f ¼ 1.0)

Algorithm Rank 1 Rank 2 $ Rank 3 SMR AMP

Hybrid graph 49 1 0 0.980 1.000MCAG only 47 2 1 0.940 0.999SVG only 47 1 2 0.940 0.999

Table 2Indexing result with Swain’s image (32 inputs, 66 models,f ¼ 1.0)

Algorithm Rank 1 Rank 2 $ Rank 3 SMR AMP

Hybrid graph 32 0 0 1.000 1.000MCAG only 31 1 0 0.969 1.000SVG only 30 0 2 0.938 0.998Swain’s 29 3 0 0.907 0.998


retrieval. In addition, in order to take the overall rank intoaccount, the AMP,h, is also defined as [2]

h¼1M

∑Mi ¼ 1

N ¹ Ri

N ¹ 1(17)

where N and M denote the number of model and inputimages, respectively, andRi is the rank of theith inputquery. If all the input queries are perfectly retrieved, thenh would be 1, whileh decreases to 0 as the count of thepoorly retrieved queries increases.

Let us consider 32 images, which are shown in Fig. 8, forthe input query to Swain’s database. Notice that the objectsin the input query are distorted by deformation, occlusion,and scaling. The results are presented in Table 2, in which itis shown that the hybrid graph approach yields the perfect

result. In addition, it is observed that either MCAG or SVGalone also provides a satisfactory result, which is even betterthan Swain’s.

The matching performance is also evaluated on theVirage database. There are 104 images in the database,and attempts are made to retrieve 50 input queries, whichare shown in Fig. 10. in this case, the distortion is muchmore severe than the Swain’s images. The final result isprovided in Table 3. It is observed that the result is perfect,with one exception: the query, retrieved, and the correctanswer are also shown in Fig. 11. As shown in Fig. 11,there are many small objects scattered randomly, makingeach chromatic region very thin and noisy. Thus, it isbelieved that the majority operator probably fails in thiscase. As a result, the resultant MCAG and SVG provideincorrect information about the chromatic regions.

To examine the real environment, attempts are also madeto retrieve similar images for a large database. The databasecontains more than 1000 images. The results are shown inFig. 12. In Fig. 12, the leftmost image is the query and thosefollowing to the right are the retrieved images ordered bytheir similarity. Note that the computational complexity isalso tolerable. It takes about 1 s for an image to be retrieved.

In the final experiment, we attempt to reduce the size ofthe graph, while maintaining the indexing performance. As

Fig. 11. Incorrect result: (a) query image; (b) retrieved image; (c) correctanswer.

Fig. 12. Search results for similar images.


described in Section 2, a node is considered to be effective,if the node label is greater than the thresholdt given inEq. (2). The average number of effective nodes is computedfor Swain’s database as varying thef from 1.0 to 0. Asfdecreases, the number of effective nodes decreasesdramatically, as illustrated in Fig. 13. For example, iff ¼

0.7, i.e., 70% of total pixels are used for generating thegraph, we can see that only 17 nodes are sufficient forrepresenting the image. Although the graph size is reduced,it is observed that there is only slight degradation in theindexing performance. Table 4 and Table 5 demonstratethe indexing results using several choices off with Swain’sand the Virage database, respectively.

4. Conclusions

In this paper, we presented a novel algorithm to retrieve

color images using their contents. A hybrid graph represen-tation—MCAG and SVG—is proposed to construct thefeatures, making use of regional adjacency and the spatialdistribution of each color region in the image. The proposedalgorithm was validated in the experiments, by testing theboth Swain’s and the Virage databases. It was observed thatthe proposed algorithm works fairly well for the poor inputset and the large database. In addition, the proposed graphrepresentation is attractive, since it reduces the image datasignificantly. Therefore, it could be relevant for utilizationwhen searching and retrieving images in a remote digitallibrary through the network.

Another area of future work will be object recognitionproblem using global and local graphs, as well as multiplegraph representation, which can employ other features, suchas texture and shape. In parallel with the feature construc-tion, further investigation is required for problems relatingto the capacity of the retrieval algorithm.

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